Longley-Rice Model

Unlike smooth-earth models, Longley-Rice ingests a Digital Elevation Model (DEM) to extract a radial path profile between transmitter and receiver. It computes terrain irregularity (Δh) —the interdecile range of terrain heights along the path—to statistically characterize diffraction loss. This allows the model to distinguish between line-of-sight, diffraction, and troposcatter regimes based on actual geomorphology rather than idealized assumptions.

The algorithm dynamically selects between three distinct physical mechanisms based on path geometry and distance:

• Line-of-Sight (LOS): Direct ray with two-ray multipath reflection from smooth earth, modified by terrain roughness.
• Diffraction: Knife-edge and rounded-obstacle loss computed via the Epstein-Peterson or Deygout methods for paths obstructed by terrain.
• Tropospheric Scatter: Forward scatter from atmospheric turbulence, dominant beyond the radio horizon, modeled using the NBS-101 formulation. The model blends these modes at transition distances to avoid discontinuities.

Longley-Rice requires surface refractivity (Ns) as a climate parameter, typically derived from ITU-R P.453 maps. Refractivity governs the effective Earth radius factor (k-factor) and determines the degree of ray bending. The model uses this to calculate the radio horizon distance and to adjust the long-term fading statistics. Standard inputs include Ns=301 for temperate continental climates and Ns=370 for tropical maritime regions.

Rather than a single deterministic loss value, the model returns median transmission loss along with three variability components:

• Time Variability (σt): Hour-to-hour fading due to atmospheric changes.
• Location Variability (σl): Spatial variation from terrain and clutter differences at the receiver.
• Situation Variability (σs): Combined uncertainty for predicting service probability. This enables engineers to compute fade margins for desired reliability percentages (e.g., 90%, 99%, 99.9%).

The model is empirically validated for 20 MHz to 20 GHz, covering VHF, UHF, and SHF bands. Key constraints include:

• Path lengths from 1 km to 2000 km.
• Antenna heights between 0.5 m and 3000 m above terrain.
• Not designed for short-range indoor or dense urban microcell predictions—ray-tracing engines are preferred for those scenarios.
• Does not model ducting or anomalous propagation layers explicitly, which can cause significant prediction errors in coastal environments.

Longley-Rice serves as the foundational propagation engine in several regulatory tools:

• Spectrum Access System (SAS) for CBRS 3.5 GHz band: Computes protection contours for incumbent federal radar systems.
• TV White Space (TVWS) databases: Predicts coverage of broadcast transmitters to identify unused channels.
• FCC's OET Bulletin 69: Recommends ITM for broadcast auxiliary and fixed microwave coordination.
• Radio Environment Maps (REM): Provides the path loss layer for interpolating signal strength between sensor measurements.

Longley-Rice operates in two distinct prediction modes that serve different engineering requirements:

Point-to-Point Mode

• Requires a precise terrain path profile between specific transmitter and receiver coordinates
• Accounts for individual diffraction obstacles along the path
• Used for fixed-link budget analysis and site-specific coverage verification

Area Mode

• Estimates median path loss over a generalized terrain without a specific path profile
• Uses statistical terrain parameters like Δh (interdecile range) to characterize roughness
• Suitable for broadcast coverage planning and generalized service contour prediction
• Computationally faster but less precise than point-to-point analysis

The model requires surface refractivity (Ns) as a critical input parameter, typically derived from ITU-R Recommendation P.453. This value determines the effective Earth radius factor (k-factor) and influences:

• Tropospheric scatter predictions beyond the radio horizon
• Ducting conditions where signals become trapped in atmospheric layers
• Time variability statistics for different climate regions

Standard reference atmospheres include:

• Continental temperate: Ns ≈ 301 N-units
• Maritime tropical: Ns ≈ 370 N-units
• Desert: Ns ≈ 280 N-units

Incorrect refractivity assumptions can introduce errors exceeding 10 dB in beyond-line-of-sight predictions.

Ground electrical characteristics significantly affect vertically polarized signals at frequencies below 1 GHz. The model accepts:

• Relative permittivity (εr): Dielectric constant of the surface material
• Conductivity (σ): Measured in Siemens per meter

Typical values by terrain type:

• Sea water: εr = 81, σ = 5.0 S/m (excellent ground plane)
• Fresh water: εr = 80, σ = 0.01 S/m
• Good soil: εr = 15, σ = 0.005 S/m
• Dry sand: εr = 3, σ = 0.0001 S/m (high ground-wave attenuation)

These parameters primarily affect ground-wave propagation and become negligible above approximately 1 GHz where surface wave attenuation dominates.

Longley-Rice outputs are statistical, not deterministic. The model provides three variability quantiles:

• Time variability (σt): Accounts for atmospheric changes over hours to seasons. A 50% time availability means the predicted loss is exceeded half the time.
• Location variability (σl): Models signal variation across a 100m x 100m area due to local clutter and multipath. Typically 8-12 dB standard deviation in urban environments.
• Situation variability (σs): Combined uncertainty when both time and location are considered simultaneously.

Engineers typically design links for 90-99.9% time and location reliability, adding fade margins of 10-30 dB above median predictions.

Longley-Rice occupies a specific niche in the propagation modeling landscape:

vs. Hata/COST-231

• Hata models are empirical and valid only for specific antenna heights and urban morphologies
• Longley-Rice is semi-empirical with physics-based diffraction, valid for any terrain

vs. Okumura

• Okumura requires extensive correction factors for terrain types
• Longley-Rice directly ingests terrain profiles

vs. Ray Tracing

• Ray tracing provides deterministic multipath predictions using 3D building data
• Longley-Rice predicts median path loss without resolving individual multipath components

vs. Free Space + Diffraction

• Simple knife-edge models ignore troposcatter and atmospheric effects
• Longley-Rice includes these mechanisms for beyond-horizon predictions